Respuesta :
Answer :
The number of gold atoms in nanogram is, [tex]3.057\times 10^{12}[/tex]
The number of gold atoms in picogram is, [tex]3.057\times 10^{9}[/tex]
Explanation :
As we know that the molar mass of gold is, 196.97 g/mole. That means, 1 mole of gold has 196.97 grams of mass of gold.
As we know that,
1 mole contains [tex]6.022\times 10^{23}[/tex] number of atoms.
First we have to determine the number of gold atoms in a nanogram.
As, 196.97 grams of gold contains [tex]6.022\times 10^{23}[/tex] number of gold atoms
And, 1 grams of gold contains [tex]\frac{1g}{196.97g}\times (6.022\times 10^{23})[/tex] number of gold atoms
So, [tex]10^{-9}[/tex] nanograms of gold contains [tex]\frac{1g}{196.97g}\times (10^{-9})\times (6.022\times 10^{23})=3.057\times 10^{12}[/tex] number of gold atoms
The number of gold atoms in nanogram is, [tex]3.057\times 10^{12}[/tex]
Now we have to determine the number of gold atoms in a picogram.
As, 196.97 grams of gold contains [tex]6.022\times 10^{23}[/tex] number of gold atoms
And, 1 grams of gold contains [tex]\frac{1g}{196.97g}\times (6.022\times 10^{23})[/tex] number of gold atoms
So, [tex]10^{-12}[/tex] picograms of gold contains [tex]\frac{1g}{196.97g}\times (10^{-12})\times (6.022\times 10^{23})=3.057\times 10^{9}[/tex] number of gold atoms
The number of gold atoms in picogram is, [tex]3.057\times 10^{9}[/tex]
